Question

Найдите значение выражения: 
(pq/p+q) * (q/p-p/q)   при p=3-2√2, q=-2√2

Answer 1

$( frac{pq}{p+q})*( frac{q}{p}- frac{p}{q})=(frac{pq}{p+q})*(frac{qp-p^{2}}{qp})= \ \ frac{pq(qp-p^{2})}{qp(p+q)}= frac{p^{2}q(q-p)}{qp(p+q)};\\\ frac{(3-2 sqrt{2})^{2}*(-2 sqrt{2})(-2 sqrt{2}+3-2 sqrt{2})}{(-2 sqrt{2})*(3-2 sqrt{2})(3-2 sqrt{2}-2 sqrt{2})}= frac{(3-2 sqrt{2})(3-4 sqrt{2})}{(3-4 sqrt{2})}=3-2 sqrt{2}$